Interpreting the Coefficients in Dynamic Two-Way Fixed Effects Regressions with Time-Varying Covariates

This paper discusses the causal interpretation of event study coefficients in a dynamic two-way fixed effects regression with time-varying covariates under a conditional parallel trends assumption. In addition to the “cross-lag contamination” problem noted by Sun and Abraham (2021), we find a new source of bias induced by the time-varying effect of the covariates. This covariate effect bias will not be eliminated even under treatment effect homogeneity and will remain in the canonical two-period difference-in-differences setting